If , are respectively arithmetic means of squares and cubes of all the numbers less than n and prime to it, prove that
My Self Assessment
Find the sum of the series to infinity
Sum to n terms
Sum to n terms, the series 1, 6, 15, 28, . . . . .
Solve the equation
Sum the series
Sum the series 6 + 9 + 14 + 23 + 40 + . . . . . to n terms
Sum the series to n terms
Sum of the series to infinity
Show that if a, b, c, d be four positive unequal quantities and then .
Sum of the series
Find the nth term and the sum of n terms of the recurring series to n terms.
If two roots of the equation be equal and of opposite sign, show that pq = r.
Sum the following series to n terms
Solve the equation having one root as
Form an equation whose roots shall be the product of every two roots of
Two numbers a and b are given, two other numbers and are formed by the relation , Two more , are formed from , in the same manner and so on. Find in terms of a and b and prove that when n is infinite
If a, b, c are real positive quantities, show that
If , prove that a, b, c are in harmonic progression, unless b = a + c .
If are any four consecutive coefficients of extended
binomial, prove that
A purchaser is to take a plot of land facing a street, the plot is to be rectangular and three times the frontage added to twice its depth is to be 26 meters. What is the greatest number of square meters he may take?
Show that
Having given , expand x in form and show that
